{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "# @author: tongzi\n",
    "# @created date: 2019/10/09\n",
    "# @description: featur engineering\n",
    "# @last modification: 2019/10/9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果说朴素贝叶斯（详情请参见 5.5 节）是解决分类任务的好起点，那么线性回归模型就\n",
    "是解决回归任务的好起点。这些模型之所以大受欢迎，是因为它们的拟合速度非常快，而\n",
    "且很容易解释。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5.6.1简单的线性回归\n",
    "拟合一条直线：  \n",
    "$$ y = ax + b$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "举例，假设a=2, b=-5:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xb138940>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb04eeb8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(0)\n",
    "x = 10 * rng.rand(50)\n",
    "y = 2 * x - 5 + rng.randn(50)\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "model =  LinearRegression(fit_intercept=True)\n",
    "model.fit(x[:,None], y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xb6476d8>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb653828>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xfit = np.linspace(0, 10, 1000)\n",
    "yfit = model.predict(xfit[:, None])\n",
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, yfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "数据的斜率和截距都在模型的拟合参数中，Scikit-Learn 通常会在参数后面加一条下划线，即 coef_ 和 intercept_ ："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model slope (斜率): 1.9692732947309524\n",
      "Model intercept (截距): -5.007210084130277\n"
     ]
    }
   ],
   "source": [
    "print('Model slope (斜率):', model.coef_[0])\n",
    "print('Model intercept (截距):', model.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "然而， LinearRegression 评估器能做的可远不止这些——除了简单的直线拟合，它还可以处理多维度的线性回归模型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = rng.rand(1000, 4)\n",
    "# 多项式：y=1.5x_1 - 3x_2 + 2x_3 - x_4\n",
    "y = 0.5 + X @ [1.5, -3, 2, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model coefficients (系数): [ 1.5 -3.   2.  -1. ]\n",
      "Model intercept (截距): 0.4999999999999993\n"
     ]
    }
   ],
   "source": [
    "model.fit(X, y)\n",
    "print('Model coefficients (系数):', model.coef_)\n",
    "print('Model intercept (截距):', model.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中 y 变量是由4个随机的 x 变量线性组合而成，线性回归模型还原了方程的系数。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5.6.2基函数回归  \n",
    "你可以通过基函数对原始数据进行变换，从而将变量间的线性回归模型转换为非线性回归模型。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 1.多项式基函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.,  4.,  8.],\n",
       "       [ 3.,  9., 27.],\n",
       "       [ 4., 16., 64.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([2, 3, 4])\n",
    "poly = PolynomialFeatures(degree=3, include_bias=False)\n",
    "poly.fit_transform(x[:, None])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "转换器通过指数函数，将一维数组转换成了三维数组。这个新的高维数组之后可以放在多项式回归模型中。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "数据经过转换之后，我们就可以用线性模型来拟合 x 和 y 之间更复杂的关系了。例如，下面是一条带噪的正弦波:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(0)\n",
    "x = 10 * rng.rand(100)\n",
    "y = np.sin(x) + rng.randn(100) * 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xbb6d7f0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb1893c8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "model = make_pipeline(PolynomialFeatures(degree=8), LinearRegression())\n",
    "model.fit(x[:, None], y)\n",
    "yfit = model.predict(xfit[:, None])\n",
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, yfit)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.高斯基函数  \n",
    "有一种常用的拟合模型方法使用的并不是一组多项式基函数，而是一组高斯基函数：  \n",
    "![image.png](attachment:image.png)  \n",
    "图 中的阴影部分代表不同规模基函数，把它们放在一起时就会产生平滑的曲线。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.base import BaseEstimator, TransformerMixin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GaussainFeatures(BaseEstimator, TransformerMixin):\n",
    "    def __init__(self, N, width_fator=2.0):\n",
    "        self.N = N\n",
    "        self.width_fator = width_fator\n",
    "        \n",
    "    @staticmethod\n",
    "    def _gauss_basis(x, y, width, axis=None):\n",
    "        arg = (x - y) / width\n",
    "        return np.exp(-0.5 * np.sum(arg**2, axis))\n",
    "    \n",
    "    def fit(self, X, y=None):\n",
    "        #在数据区间创建N的高斯分布中心\n",
    "        self.centers_ = np.linspace(X.min(), X.max(), self.N)\n",
    "        self.width_ = self.width_fator * (self.centers_[1] - self.centers_[0])\n",
    "        return self\n",
    "    \n",
    "    def transform(self, X):\n",
    "        return self._gauss_basis(X[..., None], self.centers_, \n",
    "                                 self.width_, axis=1)\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('gaussainfeatures', GaussainFeatures(N=20, width_fator=2.0)), ('linearregression', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False))])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gauss_model = make_pipeline(GaussainFeatures(20), LinearRegression())\n",
    "gauss_model.fit(x[:, None], y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xbb72be0>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbb72ba8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "yfit = gauss_model.predict(xfit[:,None])\n",
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, yfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5.6.3正则化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "虽然在线性回归模型中引入基函数会让模型变得更加灵活，但是也很容易造成过拟合（详情请参见 5.3 节）。例如，如果选择了太多高斯基函数，那么最终的拟合结果看起来可能并不好："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 3.5)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbdb4710>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gauss_model = make_pipeline(GaussainFeatures(60), LinearRegression())\n",
    "gauss_model.fit(x[:, None], y)\n",
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, gauss_model.predict(xfit[:,None]))\n",
    "plt.xlim(0, 10)\n",
    "plt.ylim(-1.5, 3.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果将数据投影到 60 维的基函数上，模型就会变得过于灵活，从而能够适应数据中不同位置的异常值。如果将高斯基函数的系数画出来，就可以看到过拟合的原因:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def basis_plot(model, title=None):\n",
    "    fig, ax = plt.subplots(2, sharex=True)\n",
    "    model.fit(x[:,None], y)\n",
    "    \n",
    "    ax[0].scatter(x, y)\n",
    "    ax[0].plot(xfit, model.predict(xfit[:,None]))\n",
    "    ax[0].set(xlabel='x', ylabel='y', ylim=[-1.5, 3.5])\n",
    "    \n",
    "    if title:\n",
    "        ax[0].set_title(title)\n",
    "        ax[1].plot(model.steps[0][1].centers_, model.steps[1][1].coef_)\n",
    "        ax[1].set(xlabel='basis location', ylabel='coefficient')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcfcc470>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = make_pipeline(GaussainFeatures(60), LinearRegression())\n",
    "basis_plot(model, 'gauss_basis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "下面那幅图显示了每个位置上基函数的振幅。当基函数重叠的时候，通常就表明出\n",
    "现了过拟合：相邻基函数的系数相互抵消。这显然是有问题的，如果对较大的模型参数进行惩罚（penalize），从而抑制模型剧烈波动，应该就可以解决这个问题了。这个惩罚机制被称为正则化（regularization），有几种不同的表现形式。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 1.岭回归（$L_2范数正则化$）  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "正则化最常见的形式可能就是岭回归（ridge regression，或者 $L_2$ 范数正则化），有时也被称为吉洪诺夫正则化（Tikhonov regularization）。其处理方法是对模型系数平方和（$L_2$ 范数）进行惩罚，模型拟合的惩罚项为：  \n",
    "$$ P = \\alpha \\sum_{n=1}^N \\theta_n^2 $$  \n",
    "其中，$\\alpha$是一个自由参数，用来控制惩罚的力度。这种带惩罚项的模型内置在 Scikit-Learn的 Ridge 评估器中："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd066cc0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import  Ridge\n",
    "model = make_pipeline(GaussainFeatures(60), Ridge(alpha=0.1))\n",
    "basis_plot(model, 'gauss basis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参数$\\alpha$是控制最终模型复杂度的关键。如果$\\alpha$→0，那么模型就恢复到标准线性回归结果；如果 $\\alpha$ → $\\infty$，那么所有模型响应都会被压制。岭回归的一个重要优点是，它可以非常高效地计算——因此相比原始的线性回归模型，几乎没有消耗更多的计算资源。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.Lasso正则化($L_1范数$)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "另一种常用的正则化被称为 Lasso，其处理方法是对模型系数绝对值的和（$L_1$ 范数）进行惩罚：  \n",
    "$$ P = \\alpha \\sum_{n=1}^N |\\theta_n| $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "虽然它在形式上非常接近岭回归，但是其结果与岭回归差别很大。例如，由于其几何特\n",
    "性，Lasso 正则化倾向于构建稀疏模型；也就是说，它更喜欢将模型系数设置为 0。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd066588>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "model = make_pipeline(GaussainFeatures(60), Lasso(alpha=0.001))\n",
    "basis_plot(model, 'gauss basis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过 Lasso 回归惩罚，大多数基函数的系数都变成了 0，所以模型变成了原来基函数的一小部分。与岭回归正则化类似，参数$\\alpha$控制惩罚力度，可以通过交叉检验来确定。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5.6.4预测自行车流量"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
